07. element managerapprval: - c date iti

. 0

SOFTWARE RELEASE NOTICE

.SRNNumerCSRC-01. SRN Number: SRN-283

02. Project Title: Evolution of Near-field Environment: Project No.:20.06002.01.072

l03. SRN Title: MULTIFLO V1.5.2

04. Originator/Requestor: Scott Painter Date:1l1/12//02

05. Summary of Actions

a Release of new software

* Release of modified software:D Enhancements made

* Corrections made

E Change of access software

[1 Software Retirement

06. Persons Authorized Access

Name RO/RW A/C/D

Scott Painter RW

L Browning RO

R. Green RO

G. Ofoegbu RO

R. Pabalan RO

C. Manepally RO

M. Seth RW

07. Element ManagerApprval: - C Date / itI

08. Remarks:V

CNWRA Form TOP-6 (06/95)

0

SOFTWARE SUMMARY FORM

01. Summary Date: 02. Summary prepared by (Name and phone) 03. Summary Action:11/12/2002 Scott Painter, 522-3348

New04. Software Date: 05. Short Title:

11/12//2002 MULTIFLO Version 1.5.2

06. Software Title: 07. Internal SoftwareID:

MULTIFLO Version 1.5.2 NONE

08. Software Type: 09. Processing Mode: 10. APPLICATION AREAa. General:

o Automated Data System 0 Interactive * Scientific/Engineering * Auxiliary Analyses0 Total System PA

* Computer Program 0 Batch 0 Subsystem PA 0 Other

o Subroutine/Module * Combination b. Specific:Groundwater multiphase flow and reactive transportmodel

11. Submitting Organization and Address: 12. Technical Contact(s) and Phone:

CNWRA6220 Culebra Road Scott Painter, (210) 522-3348San Antonio, TX 78228 l

13. Narrative:The code is used to model multiphase groundwater flow and reactive transport. |

14. Computer Platform 15. Computer Operating 16. Programming Language(s): 17. Number of SourceSystem: Program Statements:

SUN UNIX Fortran 77 -70,000

18. Computer Memory 19. Tape Drives: 20. Disk/Drum Units: 21. Graphics:Requirements:

Problem Dependent N/A N/A ASCII plot data files

22. Other Operational RequirementsThermodynamic database required.

23. Software Availability: 24. Documentation Availability:

03 Available * Limited 0 In-House ONLY * Available 0 Inadequate 0 In-House ONLYDRAFT

Software Developer: / 1 Date: ! /11 -0 al

CNWRA Form TOP-4-1

CENTER FOR NUCLEAR WASTE REGULATORY ANALYSESQA VERIFICATION REPORT

FOR-#DEVELOPED OR ACQUIRED TO BE MODIFIED SOFTWARE 4-

Software Title/Name: s r4!SoA Js A a. z.Version: A 5 Z

Demonstration workstation: 4: S'/Z°9 B/+ . POperating System: ___

Developer: ;. , a , : io

Software Requirements Description (SRD) [TOP-01 8, Section 5.3]

SRD Version: 2 0SRD Approval Date: ___Z__//_9_ _ _ _ _

SRD and any changes thereto reviewed in accordance with QAP-002 requirements?

Yes:X No: J N/A: O

Is a Software Change Report(s) (SCR) used for minor modifications (i.e., acquired code), problems or changes to aconfigured version of software?

Ad sChy< - 44 6 Z7xd. Yes:p' No: O N/A: OComments:

Software Development Plan (SDP) [TOP-0 18, Section 5.4]

SDP Version: As,-q- a/SDP (EM) Approval Date: Z t!!!

The SDP addresses applicable sections of TOP-018, Appendix B, SDP Template?

Yes:% No: O N/A: 7

Is the waiver (if used) in accordance with specified guidelines?

Yes: O No: 0 N/A:XComments:

Design and Development [TOP-018, Section 5.5.1 - 5.5.4]

Is code development in accordance with the conventions (i.e., coding conventions)described in the SDP/SCR?

Yes: No: I N/A: OModule(s) Reviewed:

Comments:a 0 ,> r£,/ 'vsjZ4~17*~ -ju 7Stdo5~Ei~y 4

, a.irPjdA corns7.v

(04/01) Page 1 of 5


FOR-#DEVELOPED OR ACQUIRED TO BE MODIFIED SOFTWARE -

Is code internally documented to allow a user to understand the function(s) being performed and to follow the flowof execution of individual routines?

Yes:) No: O N/A: O

Module(s) Reviewed:

Comments:gaus74~ s aIL/6I*

Is development of the code and informal module/subroutine-level testing documented in scientific notebook and/orSCR?

Yes:,W No: O N/A: O3SCR's and/or Scientific Notebook(s) Reviewed: 27Zi-

Comments: Ad Cf3 g41 {V A.1

Software designed so that individual runs are uniquely identified by date, time, name of software and version?

Date and Time Displayed: idA 1011 4t /4: /0 . o Z YesVX No: 0I N/A: 2Name/Version Displayed: &/Lr/PCL 0 2l d /. S Z ,dOL_ 2Q -

Comments:

Medium and Header Documentation [TOP-018, Section 5.5.6]

A program title block of main program contains: Program Title, Customer Name, Customer Office/Division, CustomerContact(s), Customer Phone Number, Associated Documentation, Software Developer and Phone Number, Date, andDisclaimer Notice?

Yes:X No: r N/A: OComments: Soi 4 "A ;

Source code module headers contain: Program Name, Client Name, Contract reference, Revision Number, RevisionHistory, and Reference to SRD/SCR requirement(s)? Yes.X No: 0 N/A: 0

Module(s) Reviewed: 4ait. ,

Comments:

The physical labeling of software medium (tapes, disks, etc.) contains: Program Name, Module/Name/Title, ModuleRevision, File type (ASCII, OBJ, EXE), Recording Date, and Operating System(s)?

Yes: No: 0 N/A: EComments:

Page 2 of 5(04/01)


FOR-DEVELOPED OR ACQUIRED TO BE MODIFIED SOFTWARE 4-

Code Reviews [TOP-0 18, Section 5.5.6]

Are code reviews (if implemented) documented in a scientific notebook or in another format that allows others tounderstand the code review process and results? N/AX

Yes: O No: O NAI

Documented in Scientific Notebook No.: ZA-*Comments: A. fi,/- .,t#/

i0 s

Acceptance and Installation Testing [TOP-018, Section 5.6]

Does acceptance testing demonstrate whether or not requirements in the SRD and/or SCR(s) have been fulfilled?

St 40,jj9 MS ACe 1 p« Cf iS0 Gy'Yes:X No: 1 N/A: O

Has acceptance testing been conducted for each intended computer platform and operating system?

A#V' 0 SO/e Yes:> No: 0 N/A: 0

Computer Platforms: _______Operating Systems: &Al;'( A 17r

Location of Acceptance Test Results: CI OA 7?i ya;Ce

Comments:

Has installation testing been conducted for each intended computer platform and operating system?

og,2,/,.4 eYesX No: J N/A: f

Computer Platforms: z Aj2o Operating Systems: x' o 0&6b A 7/T

Location of Acceptance Test Results: dOJ £e o /

Comments:

User Documentation [TOP-01 8, Section 5.5.7]

Is there a Users' Manual for the software and is it up-to-date?A lto_;,C40 ashIt 0~d Yes:* No: Cl N/A: 0

User's Manual Version and Date: .5 Z."/ 2oecu IT

Comments: Cl /t 1k ''z 4*ok~7 #x/

(04/01) Page 3 of 5

0 0


FOR-#DEVELOPED OR ACQUIRED TO BE MODIFIED SOFTWARE 4

Are there basic instructions for the installation and use of the software?

-:?,f ~ ~~~~~~~Yes:> No: O N/A: OLocation of Instructions: OJ e 6 '4" Ig2 7 sCNo-: N :

Af ac -X / f ~ -_/Gsto /4Comments: 4

Configuration Control [TOP-018, Section 5.7, 5.9.3]

Is the Software Summary Form (Form TOP-4-1) completed and signed? Y No: C3 N/A: El} ~~~~~~~~~~~~~Yes:)4 N:O NA

Date of Approval: / Z ZC. -

Is the list of files attached to the Software Summary Form complete and accurate?

Comments: c Jf Yes:> No:El N/A:E

Is the source code available or, is the executable code available in the case of (acquired/commercial codes)?

-2t ~~~~Yes:,> No: O N/A: OLocation of Source Code: s No:s 4 V N/Ai:i 4

Comments:

Have all the script/make files and executable files been submitted to the Software Custodian?

Location of script/make files: / Yes; No: E N/A: Ch

Comments: 42 S H

Software Release [TOP-0 18, Section 5.9]

Upon acceptance of the software as verified above, has a Software Release Notice (SRN), Form TOP-6 been issuedand does the version number of the software match the documentation?

Yes:'" No: O N/A: E

SRN Number: 8 13Comments:

(04/01) Page 4 of 5

0


FOR-DEVELOPED OR ACQUIRED TO BE MODIFIED SOFTWARE 4-

Software Validation [TOP-0 18, Section 5.10]

Has a Software Validation Test Plan (SVTP) been prepared for the range of application of the software?

Yes:'V No: C3 N/A: 0

Version and Date of SVTP: 7 Go 7Z St/7iW 64- IA Bt 44'/A. / Adz A£ 4

Date Reviewed and Approved via QAP-002: 7/Z// /. X z.

Comments: SC2 ar X COME. k' 4uL7l'o / J14/ ; , .4- X V

Has a Software Validation Test Report (SVTR) been prepared that documents the results of the validation caseinterpretation of the results, and determination if the software has been validated?

Yes: 0 No: N/A: OVersion and Date of SVTR:

Date Reviewed and Approved via QAP-002:

Comments:

Additional Comments:

Qc" : I' -L KZ 2••Software Developer/Date Software Custodian/Date

////4/. a Z-

(04/01) Page 5 of 5

c*file bndcond.f

c Program Name: MULTIFLO/GEMc File/Subroutine Name: bndcond.f

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Release Date:Release Version:Client Name:Client Contact:Contract Number:CNWRA Contact:

November 20021.5.2USNRCJohn Bradbury (301-415-6597)NRC 02-97-009Scott Painter (210-522-3348)Center for Nuclear Waste Regulatory AnalysesSan Antonio, Texas [email protected]

cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

c VERSION/REVISION HISTORY

c $Id$c $Log$

c-------------------c Date Author(s) Comments/Modificationsc-___________________

c April 97cc

Peter C. LichtnerMohan S. Seth

Initial Implementation

c SCR-351cc

2002 Mohan S Seth revised to treat individualgrid blocks for coupled runs

c November 2002 Scott Painter SCR406 Item 4cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

c DISCLAIMER/NOTICE

c This computer code/material was prepared as an account of workc performed by the Center for Nuclear Waste Regulatory Analyses (CNWRA)c for the Division of Waste Management of the Nuclear Regulatoryc Commission (NRC), an independent agency of the United Statesc Government. The developer(s) of the code nor any of their sponsorsc make any warranty, expressed or implied, or assume any legalc liability or responsibility for the accuracy, completeness, orc usefulness of any information, apparatus, product or processc disclosed, or represent that its use would not infringe onc privately-owned rights.

c IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW WILL THE SPONSORSc OR THOSE WHO HAVE WRITTEN OR MODIFIED THIS CODE, BE LIABLE FORc DAMAGES, INCLUDING ANY LOST PROFITS, LOST MONIES, OR OTHER SPECIAL,c INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE ORc INABILITY TO USE (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATAc BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY THIRD PARTIES OR Ac FAILURE OF THE PROGRAM TO OPERATE WITH OTHER PROGRAMS) THE PROGRAM,c EVEN IF YOU HAVE BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES,c OR FOR ANY CLAIM BY ANY OTHER PARTY.


c PURPOSE:

c This routine imposes boundary conditions for implicit method,however,c it designed such that it can also be used for op. split and explicitc and other methods.


c INTERFACING ARGUMENTS:

c Variable name Type Descriptionc

c nc Integer -number of primary speciesc ppsigl Array(nc,nb), Real*8 -total concentration in aqueous orc gaseous phasec dpsi Array(nc,nc,*), Real*8 -partial derivatives of ppsic psiglbnd Array(nc,6), Real*8 -boundary condition arrayc---___________

c Externalsc =========

c none


c INTERFACING ROUTINES

c Calling routinesc

c cehyliq.fc cehytwph.fc cetvdliq.fC cetvdtwp.fc cgasos.fc cihytwph.fc cliqos.fc coshyliq.f

c Called routines Functionc ========… ======

c none

ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

c INCLUDE FILES

c Name Descriptionc ====

c impl.h -Declares real variables to real*8 and setsc frequently used constants in common.c metragem.h -Variables which are common to both metra and gemc codes.c paramtrs.h -Sets dimension limits for all variables.c scalgem.h -Scalars in common.c comgem.h -Gem-related common blocks.cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

c SYSTEM LIBRARY ROUTINES

c Name Descriptionc

c none

cccCCcCCC cCcCcCcCcCcCcccCCcccccccc c ccccCcCCccCcCCCcCC Cc CcCcCccccccCC

c OUTPUT UNIT(s)

c Unit Name(Number) Description file name

c none


c REFERENCES

c none


subroutine bndcond (nc,ncsq,ncx,ppsi,ppsig,dpsi,dpsig,dpril,dsecl,cc,cx,cdlr,vl,vg,ssat,jlc,j2c,ncc,mm2)

include 'impl.h'include 'paramtrs.h'include 'metragem.h'include 'scalgem.h'include 'comgem.h'include 'debye.h'include 'fields.h'include 'iounits.h'

dimension ppsi(nc,*), ppsig(nc,*), dpsi(ncsq,*), dpsig(ncsq,*),dpril(ncc,*), dsecl(ncx,*), cc(nc,*), cx(ncx,*),cdl(ncsq,*), r(nc,*), vl(*), vg(*), ssat(*)

dimension qk(ncmx),dq2(ncmx*ncmx),psiz(ncmx),dpsiz2(ncmx*ncmx)cms ,dqO(ncmx*ncmx)

save cvfacl, theta

data cvfacl/.018016dO/ mw of h20 * l.e-3data theta/0.9dO/

c nc = no of componets for all species

if(mm2.eq.0) thennblcl = 1nblc2 = nblkbc

elsenblcl = mm2nblc2 = mm2

endif

c print *,'iregn ',(iregngem(mm),mm=nblcl,nblc2)

do 500 mm = nblcl, nblc2

ibc = iregngem(mm)ibctype = ibndtyp(ibc)

if(ibctype.ne.l .and. ibctype.ne.3) go to 500

m2 = iblkbc(mm)if(method.eq.l.or.method.eq.3) then

im2 = m2else

im2 = 1endif

dist = distbc(ibc)area = areabc(mm)

ql = vl(mm)*area

c write (*,11) mm,m2,dist,area,vl(mm)11 format(lx,'mm nc dist area vl ',2i4,3elO.3)

if(ibctype.eq.3) thendo j = jlc, j2c

qk(j) = zeroend do

do jj = 1, ncsqdq2(jj) = zero

end dogo to 100

endif

cSCR-351: changed subscript ibc to mm on porlsbc and sgbc

if(icode.ge.3) porslbc(mm) = por(m2)*(one-sgbc(mm))

if(idif.eq.0) thenc---_____________________________c species-independent diffusion coefs

td2 = ssat(m2)*por(m2)*dpril(l,m2)c SCR406 item 4 SP 10.24.02

if(icode.eq.2) thentdl = porslbc(ibc)*dpril(l,m2)

elsetdl = porslbc(mm)*dpril(l,m2)

endif

cSCR-351: changed subscript ibc to mm on porlsbc in above line

c write (iunit2,'("tdl td2 porsl ssat por dpril ",6elO.3)')c . tdl,td2,porslbc(mm),ssat(m2),por(m2),dpril(1,m2)

if(ihrmc.eq.l) then harmonicif(tdl+td2.ne.zero) thentd = two*tdl*td2/(tdl+td2)

elsetd = zero

endifelse

td = half*(tdl+td2) arithmeticend if

trdif = td*area/dist

c write(iunit2,*) 'bndcond2: ',td,tdl,td2,area,dist

if(abs(ql).ge.theta*two*trdif .and. ifor.eq.0) then hybrid

do j = jlcj2cqk(j) = zero

end do

do jj = l,ncsqdq2(jj) = zero

end dogo to 100

endif

trdif = -trdif

do j = jlc,j2c

qk(j) = trdif*(ppsi(j,m2)-psibnd(j,ibc))

c write(iunit2,*) 'bndcondO: ',mm,trdif,delt,c . ppsi(j,m2),psibnd(j,ibc),qk(j)

end do

do jj = l,ncsqdq2(jj) = trdif*dpsi(jj,im2)

end do

elsec-____________________

c species-dependent diffusion coefs

cSCR-351: changed subscript ibc to mm on porlsbc in belowc SCR406 item 4 SP 10.24.02

if(icode.eq.2) thentdl = porslbc(ibc)

elsetdl = porslbc(mm)

end iftd2 = ssat(m2)*por(m2)

if(ihrmc.eq.l) thentrdif = two*tdl*td2/(tdl+td2)trdif = trdif/dist

elsetrdif = half*(tdl+td2)/dist arithmatic avg

endif

difmx = zerodo j = l,nc

dif = dpril(j,m2)difmx = max (difmx,dif)

end do

trdx = difmx*trdif*area

0

This file was created on: Mon Nov 4 16:10:46 200 7

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_/_/_/ _/_/ _/

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_/ _/

Developed for the U.S. NRC

VERSION 1.5.2

November 2002

MULTIPHASE-MULTICOMPONENT CHEMICAL TRANSPORT MODEL

Copyright (c) 2000 Southwest Research InstituteAll Rights Reserved

dcm demonstration with YM parameters

Aug 27, 1999

*GRID --- > Co-ordinate Geometry DCMXYZ

Number of Elements in I-direction.Number of Elements in J-direction.Number of Elements in K-direction.Total Number of Elements..........

.... NX

.... NY

.... NZ

.... NB

.. IFRQS

IPRINT. IWARN

IDEBUG

Frequency

Index forIndex for

Index for

of Short screen output...Amount of Output ........Warning Messages ........Debugging ...............

11

80160

1000011

Debugging Nodes Range ............ IBG1-IBG2 =Increments for Node-Debugging ...... IBGINC =

3

*DBAS database:/net/spock/home/spainter/multiflo/database/mastertemp.V8.R5

*OPTS Parameters Specifying Options Invoked

Index for Formulation-Method.METHODIndex for OS Algorithm ......... IOPSIndex for Finite-Differencing..IFORFlux Limitor Algorithm ...... IFLXLIM

Maximum Newtonian Iterations.. ITMAXMaximum Time-Step Cuts ...... IHALMAX

No of constant dt after cut ..NDTCMX

Index for LOG/LINEAR ........ LOGLINIndex for DELT size calcs ... ISTEPDT

Index for BCOND flux in OS ... IBCOS

2100

32161030

Index for Mineral Surf. area ..ISURF

Index for Activity Coefs ....... IACT

Stationary state ............... ISST

Upstream weight factor ......... WTUPCourant Number ............... COURNR

DELT Reduction Factor ........ DTCUTF

0

0

-10.

5.OOOOE+055. OOOE-01

c*file mainmlti.f

c Copyright 2000 Southwest Research Institute

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Program Name:File/Program Name:Other modules:

Release Date:Release Version:Client Name:Client Contact:Contract Number:CNWRA Contact:

MULTIFLOmainmlti.f/MULTIFLOblock data metragemcputim.fseconds.flnblnk.fconvert.ffrfmt.fNovember 20021.5.2USNRCJohn Bradbury (301-415-6597)NRC 02-97-009Scott Painter (210-522-3348)Center for Nuclear Waste Regulatory AnalysesSan Antonio, Texas [email protected]


c VERSION/REVISION HISTORY

c $Id$c $Log$

c---------------------c Date Author(s) Comments/Modificationsc----------------------------

c April 97cc May 98c February 2000ccc May 2000c August 2000waterccc December 2000dryoutccccprintingccc July 2001SRDc

Peter C. LichtnerMohan S. Seth

Initial Implementation

Beta Release1.2 ReleasePeter

MohanScott

C. LichtnerS. SethPainter

V1.2.1 Minor Bug fixesV1.2.2 Fix bug related to

density calculation andphase change test

V1.2.3 Fix bug related to

in GEM. Also change surfacearea update in GEM, whichwas bypassed for secondaryminerals. Minor fix to

errors.

V1.5 Section 5,7,8 of V2.0

Also assorted minor fixesSCR351SCR406

ccc

June 2002November 2002 Scott Painter


c DISCLAIMER/NOTICE

MULTIFLO, 1.5.1 LIST OF FILES, June 21, 2002

Volume in drive R is 020619_1112

Volume Serial Number is 8658-EF75V 1. .I L ,-s-6 aI

IA QC -JDirectory of R:\

06/19/0206/19/0206/19/02

11: 12a11: 12a11: 12a

<DIR><DIR><DIR> mflol. 5. 1

0 bytes3 File(s)

Directory of R:\mflol.5.1

06/19/0206/19/0206/19/0206/19/0202/21/0206/12/0206/12/0206/12/0202/21/0206/19/0202/21/0206/12/0206/12/0206/12/0206/12/02

11: 12a11: 12a11: 12a11: 12a02: 08p05: 02p02: 53p05: 02p05:20p11: 12a

02: 08p05: 02p04: 05p05: 02p05: 02p

15 File(s)

<DIR<DIRz<DIRz,<DIR7

<DIR-

AcceptanceTestsgem

20,740 gem.f

20,267 gem.obj

28,260 mainmlti.f18,787 mainmlti.obj2,470 Makefile

metra24,168 metra.f11,750 metra.obj

8,512,440 multiflo8,299,777 multiflo.exe

116,203 multiflo.map

17,054,862 bytes

Directory of R:\mflol.5.1\AcceptanceTests

06/19/0206/19/0206/19/0206/19/0206 / 19 / 02

1l:12a <DIR>

11:12a <DIR>

11:12a <DIR>

11:12a <DIR>

11:12a <DIR>

5 File(s)

AcceptanceTestlAcceptanceTest2AcceptanceTest30 bytes

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Directory of R:\mflol.5.1\AcceptanceTests\AcceptanceTestl

)6/19/02 11:12a <DIR>

)6/19/02 11:12a <DIR>

)6/12/02 04:11p 8,075 dcml_aqf5.xyp

)6/12/02 04:08p 8,075 dcmlaqm3.xyp

)6/12/02 04:06p 3,371 dcml-srfm2.xyp

)6/12/02 04:06p 3,371 dcmlsrfml.xyp

)6/12/02 04:09p 8,075 dcmlaqm4.xyp

)6/12/02 04:06p 3,371 dcmlsrff2.xyp

)6/12/02 04:06p 3,371 dcmlsrffl.xyp

)6/12/02 04:08p 5,803 dcmlsecm3.xyp

)6/12/02 04:06p 5,803 dcmlsecm2.xyp

)6/12/02 04:06p 5,803 dcmlsecml.xyp

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06/12/02 04:06p 8,075 dcml_aqm2.xyp

06/12/02 04:06p 3,530 dcml_gasm2.xyp

06/12/02 04:06p 3,530 dcmlgasml.xyp

06/12/02 04:11p 3,371 dcmlsrfm5.xyp

06/12/02 04:09p 3,371 dcmlsrfm4.xyp

06/12/02 04:08p 3,371 dcmlsrfm3.xyp

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06/12/02 04:11p 5,803 dcmlsecm5.xyp

06/12/02 04:09p 5,803 dcmlsecm4.xyp

06/12/02 04:11p 5,803 dcml_secf5.xyp

06/12/02 04:06p 5,483 dcml-volml.xyp

06/12/02 04:06p 5,483 dcmlvolm2.xyp

06/12/02 04:11p 5,483 dcml-volf5.xyp

06/12/02 04:11p 3,530 dcml-gasm5.xyp

06/12/02 04:09p 3,530 dcmlgasm4.xyp

06/12/02 04:08p 3,530 dcmlgasm3.xyp

06/12/02 04:11p 3,530 dcml gasf5.xyp

06/12/02 04:11p 5,483 dcmlvolm5.xyp

06/12/02 04:08p 5,483 dcml_volm3.xyp

06/12/02 04:09p 5,483 dcmlvolm4.xyp

05/31/02 03:41p 6,094 dcml.inp

06/12/02 04:11p 551,785 dcml.out

06/12/02 04:11p 430,857 dcml.scr

06/12/02 04:06p 8,075 dcml_aqfl.xyp

06/12/02 04:06p 8,075 dcml_aqf2.xyp

06/12/02 04:08p 8,075 dcml_aqf3.xyp

06/12/02 04:09p 8,075 dcml_aqf4.xyp

06/12/02 04:06p 3,530 dcml-gasfl.xyp

06/12/02 04:06p 3,530 dcmlgasf2.xyp

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06/12/02 04:09p 3,530 dcml-gasf4.xyp

06/12/02 04:06p 5,803 dcmlsecfl.xyp

06/12/02 04:06p 5,803 dcmlsecf2.xyp

06/12/02 04:08p 5,803 dcmlsecf3.xyp

06/12/02 04:09p 5,803 dcmlsecf4.xyp

06/12/02 04:06p 5,483 dcml-volfl.xyp06/12/02 04:06p 5,483 dcmlvolf2.xyp

06/12/02 04:08p 5,483 dcmlvolf3.xyp

06/12/02 04:09p 5,483 dcmlvolf4.xyp

05/06/02 05:18p 345 fort.22

05/06/02 05:18p 345 fort.8

02/21/02 03:22p 15,089 VAld.dat

02/21/02 03:22p 9,049 VAld.int

06/12/02 04:06p 14,460 VAldfldfl.xyp

06/12/02 04:06p 14,460 VAldfldf2.xyp

06/12/02 04:08p 14,460 VAldfldf3.xyp

06/12/02 04:09p 14,460 VAldfldf4.xyp

06/12/02 04:06p 13,405 VAldvzl.xyp

06/12/02 04:06p 13,405 VAldvz2.xyp

06/12/02 04:08p 13,405 VAldvz3.xyp

06/12/02 04:09p 13,405 VAldvz4.xyp

06/12/02 04:11p 13,405 VAldvz5.xyp

05/06/02 05:19p 13,405 VAldvz6.xyp

05/06/02 05:19p 13,405 VAldvz7.xyp

05/06/02 05:20p 13,405 VAldvz8.xyp

Page 2 of 1O

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05:20p04: llp04: llp04: 1lp04: llp04: llp04: 1lp05: 19p05:20p04: llp05: 19p04: 08p05: 19p04: 09p05:20p04: llp04: 06p05: 19p04: 06p

90 File(s)

121 VAld_errs5,849 VAldhis.xyp

147,995 VAld_out14,567 VAld_press.xyp14,567 VAld_rh.xyp14,567 VAldsat.xyp14,567 VAldtmp.xyp14,460 VAldfldf7.xyp14,460 VAldfldf8.xyp14,460 VAldfldf5.xyp

14,460 VAldfldf6.xyp

14,460 VAldfldm3.xyp14,460 VAldfldm7.xyp14,460 VAldfldm4.xyp14,460 VAldfldm8.xyp14,460 VAldfldm5.xyp14,460 VAldfldml.xyp14,460 VAldfldm6.xyp14,460 VAldfldm2.xyp

1,827,017 bytes

Directory of R:\mflol.5.1\AcceptanceTests\AcceptanceTest2

06/19/0206/19/0206/12/0206/12/0206/12/0206/12/0206/12/0206/12/0206/12/0206/12/0206/12/0206/12/0206/12/0206/12/0206/12/0206/12/0206/12/0206/12/0206/12/0206/12/0206/12/0206/12/0206/12/0206/12/0206/12/0206/12/0202/21/0206/12/0206/12/0206/12/0206/12/0206/12/0206/12/0206/12/02

11: 12a11: 12a04: 18p04: 16p04: 17p04: 16p04: 13p04: 13p04: 13p04: 18p04:13p04: 13p04: 13p04: 18p04: 17p04: 18p04: 13p04: 13p04: 18p04: 18p04: 17p04: 16p04: 18p04: 18p04: 16p04: 17p03:22p04: 18p04: 18p04: 13p04: 13p04: 16p04: 17p04: 13p

<DIR><DIR>

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578, 664472, 998

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dcml_aqf5.xypdcml_aqm3.xypdcml_aqm4.xypdcmlsecm3.xypdcml_secm2.xypdcml_secml.xypdcmlaqml.xypdcmlaqm5.xypdcmlaqm2.xypdcml-gasm2.xypdcml-gasml.xypdcml secm5.xypdcml-secm4.xypdcml_secf5.xypdcmlvolml.xypdcmlvolm2.xypdcmlvolf5.xypdcml-gasm5.xypdcml-gasm4.xypdcml-gasm3.xypdcml-gasf5.xypdcml_volm5.xypdcmlvolm3.xypdcml-volm4.xypdcml.inpdcml.outdcml.scrdcml-aqfl.xypdcmlaqf2.xypdcml_aqf3.xypdcml_aqf4.xypdcmlgasfl.xyp

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04: 13p04: 16p04:17p04: 13p04: 13p04: 16p04: 17p04: 13p04: 13p04: 16p04: 17p11:44a11: 44a03 :22p03 :22p04: 09p04: 13p04:18p04: 13p04:16p04: 17p04: 18p04: 13p04: 16p04: 13p04:18p04:18p04: 18p04: 09p04: 09p04: 17p04: 18p04: 09p04: 09p04: 18p04: 09p03:22p04: 09p03:22p04: 13p04: 13p04: 09p04: 18p04: 17p04: 16p03:22p04: 09p04: 09p04: 18p

83 File(s)

3,530 dcml-gasf2.xyp

3,530 dcmlgasf3.xyp3,530 dcml-gasf4.xyp

5,803 dcml-secfl.xyp5,803 dcml-secf2.xyp

5,803 dcmlsecf3.xyp5,803 dcml-secf4.xyp

5,483 dcml-volfl.xyp5,483 dcml-volf2.xyp5,483 dcmlvolf3.xyp

5,483 dcml-volf4.xyp345 fort.22345 fort.8

9,049 VAld.int

15,114 VAldgvt.dat121 VAldgvterrs

14,460 VAldgvtfldfl.xyp

148,883 VAldgvtout

14,460 VAldgvtfldf2.xyp



18,987 VAldgvtsat.xyp

14,460 VAldgvtfldm2.xyp


14,460 VAldgvtfldml.xyp

18,987 VAldgvttmp.xyp

18,987 VAldgvt-rh.xyp

7,617 VAldgvthis.xyp14,460 VAldgvtfldm6.xyp



14,460 VAldgvtfldm5.xyp14,460 VAldgvtfldf6.xyp

14,460 VAldgvtfldf7.xyp14,460 VAldgvtfldf5.xyp14,460 VAldgvtfldm8.xyp

14,460 VAldgvtfldm9.xyp14,460 VAldgvtfldf8.xyp14,460 VAldgvtfldf9.xyp

13,405 VAldgvtvz2.xyp13,405 VAldgvtvzl.xyp

13,405 VAldgvtvz6.xyp

13,405 VAldgvtvz5.xyp13,405 VAldgvtvz4.xyp





18,987 VAldgvt-press.xyP

1,925,003 bytes

CCCC

Directory of R:\mflol.5.1\AcceptanceTests\AcceptanceTest3

)6/19/02 11:12a <DIR>

)6/19/02 11:12a <DIR>

)6/12/02 04:40p 8,075 dcmltvdaqml.xyp

li19/lln 04:46n 8,075 dcmltvdaqm5.xypJ v / 14 / Q V .=L w_

Page 4 of 1O

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04:44p04:43p04:40p04: 46p04:40p04: 46p04:44p04:44p04:44p04:40p04: 40p04:40p04: 46p04:46p04:40p04: 46p04:43p04:40p04:40p04:40p04: 44p04: 43p04: 43p04:43p04:40p04:46p04:44p04: 40p04: 40p04:46p04:43p04: 4 0p04:44p04:43p03 :22p

04: 46p04: 46p04:40p04:40p04: 43p04: 44p03:22p03:22p03:22p04: 40p04:46p04:40p04: 43p04: 44p04:46p04:46p04:46p04: 40p03:22p04: 43p03:22p04:46p

8,0758,0758,0758,0755, 8035, 8033,5303, 5305,4835, 8033,5303, 5303,5303,5305,4835,4835, 8033,5303, 5305,4835,8033,5303, 5305,4835,8035,8035,4835, 8035,4835,4835, 8035, 4835,8035,4836, 063

574, 989465,403

8,0758, 0758,0758,0759,049

15,211121

14, 460148,88314, 46014,46014, 4607, 617

18,98718, 98713, 40513, 40513,40513, 40518,987

dcmltvd-aqm4.xypdcmltvdaqm3.xypdcmltvd-aqm2.xypdcmltvdaaqf5.xypdcmltvdsecfl.xypdcmltvdsecf5.xypdcmltvd-gasf4.xypdcmltvd_gasm4.xypdcmltvdvolf4.xypdcmltvdsecf2.xypdcmltvdgasfl.xypdcmltvd-gasml.xypdcmltvd~gasf5.xypdcmltvdgasm5.xypdcmltvdvolfl.xypdcmltvdvolf5.xypdcmltvdsecf3.xypdcmltvdgasf2.xypdcmltvdgasm2.xypdcmltvdvolf2.xypdcmltvdsecf4.xypdcmltvdtgasf3.xypdcmltvd_gasm3.xypdcmltvdvolf3.xypdcmltvdsecml.xypdcmltvdsecm5.xypdcmltvdvolm4.xypdcmltvdsecm2.xypdcmltvdvolml.xypdcmltvdvolm5.xypdcmltvdsecm3.xypdcmltvdvolm2.xypdcmltvdsecm4.xypdcmltvdvolm3.xypdcmltvd.inpdcmltvd.outdcmltvd.scrdcmltvd-aqfl.xypdcmltvdaqf2.xypdcmltvd-aqf3.xypdcmltvd-aqf4.xypVAld.intVAldgvtl.datVAldgvtlerrsVAldgvtlfldfl.xypVAldgvtloutVAldgvtlfldf2.xypVAldgvtlfldf3.xypVAldgvtlfldf4.xypVAldgvtlhis.xypVAldgvtltmp.xypVAldgvtlrh.xypVAldgvtlvz2.xypVAldgvtlvz6.xypVAldgvtlvz3.xypVAldgvtlvz7.xypVAldgvtlsat.xyp

Page 5 of 1O

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04:4 4p03:22p04:40p04: 45p03:22p03 :22p03:2 2 p03 :22p04:45p03: 22p04: 40p03:22p04:46p04: 43p03:22p04: 44p03:22p04: 40p04:45p03 :22p

81 File(s)

13,405 VAldgvtlvz4.xyp13,405 VAldgvtlvz8.xyp13,405 VAldgvtlvzl.xyp13,405 VAldgvtlvz5.xyp13,405 VAldgvtlvz9.xyp14,460 VAldgvtlfldf6.xyp14,460 VAldgvtlfldf7.xyp14,460 VAldgvtlfldf8.xyp14,460 VAldgvtlfldf5.xyp14,460 VAldgvtlfldf9.xyp14,460 VAldgvtlfldm2.xyp14,460 VAldgvtlfldm6.xyp18,987 VAldgvtl-press.xyp14,460 VAldgvtlfldm3.xyp14,460 VAldgvtlfldm7.xyp14,460 VAldgvtlfldm4.xyp14,460 VAldgvtlfldm8.xyp14,460 VAldgvtlfldml.xyp14,460 VAldgvtlfldm5.xyp14,460 VAldgvtlfldm9.xyp

1,913,119 bytes

Directory of R:\mflol.5.1\gem

06/19 /0206/19/0202 /21/0202/21/0206/12/0202/21/0206/12/0205/31 /0206/12/0202/21/0206/12/0202/21/0206/12/0202/21/0206/12/0202/21/0202/21/0202 /21/0202/21/0206/12/0202/21/0206/12/0202 /21/0202/21/0206/12/0202/21/0206/12/0202/21/0206/12/0202/21/0206/12/0202/21/0206/12/02

11: 12a11: 12a02: 07p02: 06p04: 57p02: 06p04: 57p01: 19p04: 57p02 :06p04: 57p02: 06p04: 57p02: 06p04: 57p02: 07p02: 07p02: 07p02: 06p04: 57p02: 06p04: 57p02: 07p02: 06p04: 57p02: 06p04: 57p02:06p04: 57p02: 06p04: 57p02: 06p04: 57p

<DIR><DIR>

2, 00517, 69313,2607, 080

6,252,47015,21214,41115,48218, 45924,26429,38324,73927, 6834,821

289714

13, 17412, 48744, 98968,272

14215, 64622, 66211,4348, 450

11, 12212, 68239, 44245,27112, 1089,850

addgem.hallotgem. fallotgem.objblkdtgem.fblkdtgem.objbndcond.fbndcond.objcalcpsi.fcalcpsi.objcoefimp.fcoefimp.objcoeftvd.fcoeftvd.objcomgem.hcomprs.hcxkin.hdataall.fdataall.objdatabase.fdatabase .objdebye.hderives.fderives.objelechem.felechem.objeqjac.feqjac.objeqlib.feqlib.objeqres.feqres.obj

Page 6 of 1O

02/21/0202/21/0206/12/0202/21/0202/21/0206/12/0202/21/0206/12/0202/21/0206/12/0206/12/0206/12/0202/21/0202/21/0206/12/0202/21/0206/12/0202 /21/0206/12/0202/21/0206/12/0202/21/0202/21/0206/12/0202/21/0206/12/0205/31 / 0206/12/0202/21/0206/12/0202/21/0206/12/0202/21/0202/21/ 0202/21/0206/12/0202/21/0206/12/0202/21/0206/12/0202/21/0206/12/0202/21/0202/21/0202/21/0206/12/0202/21/0206/12/0202/21/0202/21/0202/21/0202/21/0206/12/0202/21/0206/12/0205/31/0202/21/02

02: 07p02: 06p04: 57p02: 07p02: 06p04: 57p02: 06p04: 57p02: 07p03 :39p04: 58p04: 58p02: 07p02: 06p04: 57p02: 06p04: 57p02: 06p04: 57p02: 06p04: 57p02: 07p02 :06p04: 57p02: 06p04: 57p03: 04p04: 58p02:06p04: 58p02: 06p04: 58p02: 07p02: 07p02: 06p04: 58p02: 06p04: 58p02: 06p04: 58p02: 06p04: 58p02: 06p05: 23p02: 06p04: 58p02: 06p04: 58p02 :07p02 :07p02: 07p02: 06p04: 58p02 :06p04: 58p02: 50p02 :06p

310 fields.4,419 flogk.f

754 flogk.o]503 frfmt.h

9,638 gameq.f7,778 gameq.o]8,997 gamextd7,585 gamextd

72 gas.h7,590,376 gem7,617,249 gem.exe

102,880 gem.map114 gmfwt.h

23,231 graphld35,587 graphld29,790 graph2d42,376 graph2d22,176 graph3d28,859 graph3d7,493 gunits.4,601 gunits.i

179 impl.h23,613 implicil24,145 implici-31,117 imret.f36,183 imret.o}49,595 initgem73,182 initgem10,142 interpf11,203 interpf9,403 ionexc.:

11,820 ionexc.(210 iounits716 kinetic

24,904 kinrxna27,720 kinrxna16,176 kinrxns16,105 kinrxns10,078 linmonoc13,339 linmonoo12,284 luslv.f4,191 luslv.ol

24,354 maingem30,011 Makefilb9,262 massbal7,989 massbal

14,286 masstrai10,746 masstrai2,641 metragei

77 minrl.h532 ofiles.l

66,969 opsplit74,743 opsplit57,144 outgem.:89,033 outgem.(2,639 paramtrc8,505 pecletni

h

bj

bj

l obj

lfl obj

lfobj

objf.obj

t.ft. obj

* bi

f

obj~.f~.obj;h.htqf* obj;.f

;.obj.ob

:1. f-d.objZbje

.h.obj,n.f,.1objn.h

.obj

o)bjs.h

r. f

Page 7 of 10

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04: 58p02: 06p04: 58p03 :14p04: 58p02 :06p04: 58p02: 07p02: 07p02: 06p04: 58p02 :06p04: 58p02:06p04: 58p02: 06p04: 58p02 :06p04: 58p02: 06p04: 58p02: 06p04: 58p02:06p04: 58p02: 06p04: 58p02:06p04: 58p02 :07p02: 07p02:06p04: 58p01: 17p02 :05p02:06p04: 58p02 :07p03:39p04:58p02: 06p02: 06p02: 07p02: 06p04: 58p

135 File(s)

5,655 pecletnr.ob17,553 pprcgem.f18,771 pprcgem.obj47,372 readl.f52,220 readl.obj55,443 read2.f78,587 read2.obj1,486 scalgem.h

271 scratch.h10,506 setbcon.f13,116 setbcon.obj7,422 setconn.f6,451 setconn.obj7,558 solprd.f6,533 solprd.obj6,897 solprodt.f3,383 solprodt.ob

23,242 solveld.f10,799 solveld.obj10,700 speciate.f10,150 speciate.ob3,335 srcgem.f4,056 srcgem.obj

16,080 startup.f26,619 startup.obj15,846 stdyst.f12,927 stdyst.obj10,690 stepgem.f6,651 stepgem.obj354 surfkin.h300 tdconst.h

8,044 textab.f10,099 textab.obj2,209 title.h6,128 tolower

11,580 transd.f11,578 transd.obj

266 units.h8,808 updtgem.f6,307 updtgem.obj

30,439 util.f45,976 watsolv.f

388 watsolv.h6,049 zonek.f4,021 zonek.obj

23,788,585 bytes

Ij

DD

Directory of R:\mflol.5.1\metra

06/19 / 0206/19/0206/12/0206/12/0205/31/0206/12/0206/12/0206/12/02

11: 12a11: 12a11:21a04: 56p10: 17a11:21a04: 56p11:23a

<DIR><DIR>

17,2038, 8282, 54113,2455, 189

30,865

accm. faccm. objadd.hallot. fallot. objbcond. f

Page 8 of 10

i I

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04: 56p11:21a04: 56p11: 21a04: 56p10: 17a11:24a04: 56p11:21a04: 56p11: 21a04: 56p11:24a04: 56p11:21a04: 56p10: 17a11:21a04: 56p10: 17a11:21a04: 56p11:21a04: 56p11:24a04: 56p11:25a04: 56p11:21a10: 52a04: 57p04: 57p10: 17a11:21a04: 57p11:25a04: 57p10: 17a10: 17a11:22a10: 17a04: 57p11: 22a04: 57p12: 59p04: 57p11:25a04: 57p11: 22a04: 57p11:22a10: 17a04: 57p11:22a04: 57p10: 17a11: 22a

19, 4618, 095

242, 50532,38419, 8575,002

21,4768,392

18, 1004, 14721,41012, 46823, 46414, 43118,3289, 565

50312, 0496,463

17955,37746, 54715,95619, 07852, 45962, 04722,28013,45827,78210,328

1, 212, 83595, 5162, 641

12, 9076,826

35, 69932, 9842,2782,639

29, 5571, 085

16, 62432,96143,29720,06823, 9099, 3545,753

27, 62718,34919,446

56513, 71129,37627, 483

91626,420

bcond.objblkdtmet.fblkdtmet.objcoefs.fcoefs.objcom.hcond.fcond.objdtstep.fdtstep.objecmtbl.fecmtbl.objemip.femip.objequil.fequil.objfrfmt.hgriddat.fgriddat.objimpl.hinit.finit.objinpifv.finpifv.objinpmetra.finpmetra.objiter.fiter.objmainmtra.fMakefilemetra.exemetra.mapmetragem.hopenfls.fopenfls.objoutmetra.foutmetra.objparal.hparamtrs.hpckr.fpckr.hpckr.objplots.fplots.objpproc.fpproc.objprints.fprints.objpvt.fpvt.objpvtfunc.fpvtfunc.hpvtfunc.objpvth2o.fpvth2o.objpvttbl.hpvtvp.f

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06/12/02 04:57p06/12/02 11:26a06/12/02 04:57p06/12/02 11:27a

06/12/02 04:57p06/12/02 11:22a06/1'2/02 04:57p06/12/02 11:27a

06/12/02 04:57p05/31/02 11:56a06/12/02 11:22a

06/12/02 04:57p05/31/02 10:17a06/12/02 11:27a06/12/02 04:57p06/12/02 11:22a06/12/02 04:57p06/12/02 11:22a

06/12/02 04:57p06/12/02 11:22a

06/12/02 04:57p06/12/02 11:27a05/31/02 10:17a06/12/02 04:57p

96 File(s)

Total Files Listed:508 File(s)

16,221 pvtvp.obj67,434 recdat.f64,769 recdat.obj18,302 rstart.f32,386 rstart.obj1,698 scalars.h

13,245 setbc.f6,725 setbc.obj

16,320 slvlp.f7,983 slvlp.obj

10,045 solve.f2,479 solve.obj

10,689 source.f2,788 source.obj

13,587 thomas.f4,704 thomas.obj2,165 title.h

10,194 trans.f3,677 trans.obj

266 units.h8,882 update.f5,182 update.obj

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Page 10 of 10

SOFTWARE VALIDATION REPORT FORMULTIFLO VERSION 1.5.2

Prepared for

U.S. Nuclear Regulatory CommissionContract NRC-02-02-012

Prepared by

Scott Painter

Center for Nuclear Waste Regulatory AnalysesSan Antonio, Texas

February 2003

ABSTRACT

MULTIFLO is a computer code for modeling coupled thermal-hydrological-chemical processes inpartially saturated and strongly heated porous and fractured media. This software may be usedin reviewing the license application for the high-level waste repository proposed for YuccaMountain, Nevada. Eight software validation tests were conducted. These tests cover theexpected range of processes and conditions that may need to be reviewed. For all test cases,MULTIFLO Version 1.5.2 successfully reproduced the target results, which were based onanalytical, semi-analytical, or previously published solutions to the underlying mathematicalmodels. The successful validation tests suggest that the MULTIFLO Version 1.5.2 software isfunctioning properly.

iii

CONTENTS

Section Page

ABSTRACT ....................FIGURES ......................TABLES .......................ACKNOWLEDGMENTS ...........

..............

..............

..............

..............

............

............

............

............

. . . . . . . . . .. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . iii

. vii

. ix

. xi

1 INTRODUCTION.

2 SCOPE OF THE VALIDATION .

.............................

1

3 ENVIRONMENT . .............................

2

4 TEST CASES .......................... 24.1 Test 1: Multiphase Simulations of Doughty and Pruess ...... ............. 2

4.1.1 Description of the Test . ....................................... 24.1.2 Test Input and Output . ....................................... 24.1.3 Target Solution ............................................. 24.1.4 Results ............................................... 2

4.2 Test 2: Infiltration in Dual Permeability Media ........ ................... 54.2.1 Description of the Test . ....................................... 54.2.2 Test Input and Output . ....................................... 54.2.3 Target Solution ............................................. 64.2.4 Results ................................................ 7

4.3 Test 3: Drawdown in an Infinite Confined Aquifer ....... ................. 74.3.1 Description of the Test . ....................................... 74.3.2 Test Input .............................................. 74.3.3 Target Solution ............................................. 84.3.4 Results ................................................ 8

4.4 Test 4: Equilibrium Speciation in GEM ................................ 94.4.1 Description of the Test ....................................... 94.4.2 Test Input and Output ....................................... 104.4.3 Target Solution ............................................ 104.4.4 Results ................................................ 10

4.5 Test 5: Solute Transport in Dual Permeability Media .................... 104.5.1 Description of the Test ...................................... 104.5.2 Test Input and Output ....................................... 114.5.3 Target Solution ............................................ 114.5.4 Results .............................................. 12

4.6 Test 6: Three-Dimensional Advective/Dispersive Transport .124.6.1 Description of the Test .124.6.2 Test Input and Output .124.6.3 Target Solution .134.6.4 Results ............................... .13

4.7 Test 7: Fully Coupled Flow/Transport with Mineral Dissolution and PermeabilityModification ......... ............. 144.7.1 Description of the Test ..................... 14

v

CONTENTS (continued)

Section Page

4.7.2 Test Input and Output . ................................ 154.7.3 Target Solution .......... ...................... 154.7.4 Results ................................ 15

4.8 Test 8: Unstructured Grid Capability ................................ 154.8.1 Description of the Test ................................. 154.8.2 Test Input and Output . ................................ 154.8.3 Target Solution .......... ...................... 154.8.4 Results ................................ 15

5 KNOWN PROBLEMS ................................ 17

6 CONCLUSIONS ................................ 17

7 REFERENCES .......................................... 17

vi

FIGURES

Figure Page

1 Liquid Saturation Versus Boltzmann Variable for Test 1 without Vapor PressureLowering .............................................................. 4

2 Liquid Saturation Versus Boltzmann Variable for Test 1 with Vapor Pressure Lowering . 43 Temperature Versus Boltzmann Variable for Test I with Vapor Pressure Lowering .... 54 Liquid Saturation Versus Depth (Test 2). 85 Drawdown Versus Distance from Well at Two Different Times (Test 3). 96 Concentration in Mol/liter in Fractures and Matrix (Test 4) .137 One-Dimensional Traces of Concentration from the Three-Dimensional Flow-Through

Test (Test 6) ....... 148 Quartz Volume Fraction Versus Distance from Inlet for the Three Scenarios

of Test 6 .169 Drawdown Versus Distance from Well at Two Different Times (Test 8) .17

vii

0 0

TABLES

Table Page

1 Parameters for Test 1 .................................................. 32 Parameters for Test 2 ..................................... 63 Input Values for Equilibrium Constants Compared with Valued Calculated from the

Simulation Output for Test 4 ..................................... 114 Activity Coefficients from Test 4 Compared with Hand Calculations ...... ......... 115 Hydrological Parameters for Test 5 ..................................... 12

ix

0 0

x

ACKNOWLEDGMENTS

This report was prepared to document work performed by the Center for Nuclear WasteRegulatory Analyses (CNWRA) for the U.S. Nuclear Regulatory Commission (NRC) underContract No. NRC-02-97-009 and NRC-02-02-012. The activities reported here wereperformed on behalf of the NRC Office of Nuclear Material Safety and Safeguards, Division ofWaste Management. The report is an independent product of the CNWRA and does notnecessarily reflect the views or regulatory position of the NRC.

The author is grateful to C. Dinwiddie and B. Sagar for their reviews of the manuscript, and toP. Houston for formatting.

QUALITY OF DATA, ANALYSES, AND CODE DEVELOPMENT

DATA: No data were generated for this report.

ANALYSES AND CODES: This report documents quality assurance software validationactivities for MULTIFLO Version 1.5.2. MULTIFLO was developed under software qualityassurance procedure TOP-018. Calculations are documented in Scientific Notebook 282E.

xi

1 INTRODUCTION

This Software Validation Report documents software validation results for the computer codeMULTIFLO (Lichtner, 1996; Painter, et al, 2001), a numerical model describing two-phasenonisothermal flow and multicomponent reactive transport in variably saturated porous media.This software may be used in reviewing the license application for the high-level waste repositoryproposed for Yucca Mountain, Nevada.

The code can be used to analyze the drift scale and repository scale coupled thermal-hydrologic-chemical processes that could affect the performance of the proposed repository. The code canbe applied to assess processes such as

* Isothermal and nonisothermal movement of water through unsaturated rock as liquidand vapor

* The evolution of groundwater compositions near and within the engineeredbarrier system

* Changes in porosity and permeability of the host rock resulting from mineral alterationand the resulting effects on fluid transport

* Transport of aqueous and gaseous radionuclides from the waste package

The software validation tests described in this report are required by the Quality AssuranceProcedure TOP-018 and follow the procedure specified in the Software Validation Test Plan forMULTIFLO Version 1.5.1 (Painter, 2002). The validation deviates slightly from that specified inthe Software Validation Test Plan in two aspects. First, MULTIFLO Version 1.5.2 is validatedinstead of the earlier Version 1.5.1 that was specified in the Software Validation Test Plan.Second, some of the input files specified in the Software Validation Test Plan were modifiedslightly to accommodate different input requirements for the new Version1.5.2 or to correct errorsin the input file. Input and output files for the validation are on the accompanying disk.

2 SCOPE OF THE VALIDATION

This software validation is for MULTIFLO Version 1.5.2 which supersedes Version 1.5.1. TheMULTIFLO software comprises the METRA and GEM components, which can be usedseparately or in combination. Details of the software and its functioning can be found in theMULTIFLO User's Manual and in supporting technical material (Lichtner, 1996). Thisvalidation covers the major capabilities of the code that are to be used in regulatory activities.These include

1. Nonisothermal multiphase flow and phase-change phenomena in partially saturatedporous media

2. Flow in composite fractured/porous media using a dual continuum formulation

3. Flow in saturated porous media including compressibility effects

4. Advective and diffusive transport of chemicals in the aqueous and gaseous phase

1

5. Equilibrium speciation of aqueous and gaseous phase constituents

6. Kinetically controlled mineral formation and dissolution, and resulting effects on porosity,permeability, and flow

7. Unstructured grid configuration with arbitrary interblock connectivity

3 ENVIRONMENT

Validation tests were performed on the workstation farm directed by the computer knownas Idaho, which uses the Solaris 5.8 operating system. The commercial programMathematicae 4.1, running on the Windows NT (version 4) workstation Brahma, was used forsome calculations to establish target solutions to the underlying mathematical equations. Nospecial peripherals were used.

4 TEST CASES

4.1 Test 1: Multiphase Simulations of Doughty and Pruess

4.1.1 Description of the Test

These simulations are designed to test METRA's representation of nonisothermal flow,phase-change phenomena, and heat transport under transient conditions with and without vaporpressure lowering (major capability 1 in Section 2.0). The geometry is one-dimensionalcylindrical with a line heat source in the center and correspond to Figure 6 of Doughty andPruess (1992). They employ a Boltzmann transformation to reduce the partial differentialequation to an ordinary differential equation boundary value problem. They then solve theboundary value problem by the shooting method. Two test cases are considered: one with andone without vapor pressure reduction due to capillary effects. Input parameters for the test arepresented in Table 1. A grid of 400 computational cells was used for these two tests.

4.1.2 Test Input and Output

Test input files are on the accompanying disk: TestCase1knovpL.dat and TestCase1kvpL.dat.Output files are in the same directory.

4.1.3 Target Solution

The target solutions for the two simulations can be found in Figure 6 of Doughty and Pruess(1992). They employ the Boltzmann transformation approach, and rescale the radial variable

according to the Boltzmann transformation, z = Ln[r / i] , with radius r in meters and time t in

seconds. The solution then becomes a function of z only, independent of r and t.

4.1.4 Results

The case with no vapor-pressure lowering ran to completion without error. The case withvapor-pressure lowering ran to completion without error after it was modified to terminate at

2

Table 1. Parameters for Test 1.

Parameter Value

Heat source 667 W/m (0.237 Horsepower/feet)

Initial gas pressure 1 bar

Initial temperature 18 0C (64.4 1F)

Initial liquid saturation 0.8

Absolute permeability 20 x 10-'5 m2 (2.15 x 10-13ft2)

Porosity 0.10

Rock density 2550 kg/m3 (159.2 Ibm/ft3)

Specific heat 800 J/kg K (0.191 BTU/lbm 0F)

Thermal conductivity 2 W/m K (4.54 x 10-4 Horsepower/ft OF)

Tortuosity parameter 0.5

Diffusion coefficient 2.6 x 1o-5 m2/s (2.80 x 10-4 ft2/s)

van Genuchten a parameter 8.0 x 10-5 Pa-1 (8 bar 1')

van Genuchten A parameter 0.45

Residual saturation 9.6 x 10-4

Capillary pressure cutoff 5.0 x 108 Pal' (5 x 103 bar')

0.1 year. For longer simulation times, excessively large vapor-pressure reduction factors causednumerical instabilities in the case with vapor-pressure lowering. These instabilities wereobserved when temperatures exceeded 260 0C [500 'F]. This code is not expected to be usedfor temperatures of this magnitude during the regulatory reviews.

A comparison between the METRA solution and the Doughty and Pruess (1992) results for liquidsaturation is shown in Figure 1 for the case without vapor pressure lowering. The data points arefrom Doughty and Pruess (1992, Figure 6) and the curves are METRA results at t = 0.1, t = 1,and t = 6 years. The METRA curves were invariant with time, as predicted by the similaritysolution, and overlay each other on this scale over most of the range. The agreement with theDoughty and Pruess results is good over the entire range. The small differences in the locationof the hot edge of the boiling zone (relative difference of about 2 percent) is believed to be due tonumerical discretization errors in the METRA solution.

Saturation profiles for the case with vapor pressure lowering are compared in Figure 2. The datapoints are the Doughty and Pruess result (Doughty and Pruess, 1992, Figure 6) and the curve isthe METRA result at 0.1 year. The relative difference in the location of the dry-out zone, definedhere by be the position where saturation is 20 percent, is 21 percent. The agreement is good,but not exact. Exact agreement is not to be expected because of numerical discretization errorand because of minor differences in the physics models.

Temperature profiles for the case with vapor pressure lowering are compared in Figure 3. Thedata points are the Doughty and Pruess result (Doughty and Pruess, 1992, Figure 6) and the

3

10

~0.8

~0.6

C')

* 0.2

-10 -9 -8 -7Boltzmann Variable z=ln[r/t111

Figure 1: Liquid Saturation Versus Boltzmann Variable for Test I Without Vapor PressureLowering. The MULTIFLO Simulation Is Plotted as a Solid Line and the Results of

Doughty and Pruess [1992] Are Shown as Individual Data Points. The Boltzmann Variable

is Ln[r / A] Where r Is Radius in Meters and t Is Time in Seconds.

[Unit Conversion: Multiply by 1.19 to Obtain the Boltzmann Variable with Radius in Feet.]

Cl0

E 0.8

"u 0.6C')

i 0.4

i 0.2

-10Boltzmann

-9 -8 -7Variable z=ln[r/t1 1

Figure 2: Liquid Saturation Versus Boltzmann Variable for Test I with Vapor PressureLowering. The MULTIFLO Simulation Is Plotted as a Solid Line and the Results of Doughty

and Pruess [1992] Are Shown as Individual Data Points. The Boltzmann Variable is

Ln[r / At Where r Is Radius in Meters and t Is Time in Seconds.

[Unit Conversion: Multiply by 1.19 to Obtain the Boltzmann Variable with Radius in Feet.]

4

- 2500

E 1500)- 100

5~1)H 50

-10 -9 -8 -7 -6 -5Boltzmann Variable z=ln[r/t1 lg

Figure 3: Temperature Versus Boltzmann Variable for Test 1 with Vapor PressureLowering. The MULTIFLO Simulation Is Plotted as a Solid Line and the Results of Doughty

and Pruess (1992) Are Shown as Individual Data Points. The Boltzmann Variable Is

Ln[r / A] Where r Is Radius in Meters and t Is Time in Seconds. Unit Conversion:

Multiply by 1.19 to Obtain the Boltzmann Variable with Radius in Feet.[Unit Conversion: Multiply by 9/5 and 32 to Obtain Temperature in Fahrenheit.]

curve is the METRA result at 0.1 year. The agreement is excellent (<3.5 percent difference) overthe entire range of the Boltzmann variable.

4.2 Test 2: Infiltration in Dual Permeability Media


This simulation is designed to test METRA's representation of unsaturated flow in dualpermeability media (major capability 2 in Section 2.0). The geometry is one-dimensional verticalwith specified saturation at the top and bottom boundaries. The domain size is 10 m [37.8 ft] andis discretized into 100 cells of size 0.1 m (0.328 ft). The saturation at the lower boundary isspecified as 100 per cent liquid for both fractures and matrix. The saturation at the top boundaryis specified as 20 percent for the matrix and 60 percent for the fractures. van Genuchten'smodel is used to relate capillary pressure to saturation. The simulation is run until steady state isreached. The main parameters are given in Table 2.


Test input file is on the accompanying disk: TestCase2ksstate1.dat. Output files are in the samedirectory.

5

Table 2. Parameters for Test 2

Parameter Value

Matrix permeability 4 x 10-14 m2 (4.30 10-13 ft2 )

Matrix porosity 0.20

Fracture permeability (intrinsic) 4 x 10-13 m2 (4.30 10-12 ft2)

Fracture porosity 0.001

van Genuchten a parameter for matrix 1.99 X 10-3 Pa 1 (199 bar1 )

van Genuchten X parameter for matrix 0.851

van Genuchten a parameter for fracture 1.99 x 10-3 Pa-1 (199 bar-)

van Genuchten X parameter for fracture 0.851

Matrix block size 0.1 m (0.328 ft)

Fracture-to-matrix area reduction factor 10-6


The Richards equation provides an approximation to the physical situation. After setting gaspressure to atmospheric, the mass conservation equations for a single continuum reduce toRichards equation. In steady state and with one spatial dimension the dual permeabilityRichards equation can be written:

qF KFkrF( dF )

- + SFM = 0'6z

IM =-MkrM (O hM _)

_S -Hi Z FM

SFM = AFM 1KFm kid d

where z is depth, K is the saturated hydraulic conductivity, k, is the relative permeability, h is thewater pressure head in meters, and q is the volumetric flux. These are combined with twoconstitutive relations: one to relate capillary pressure with saturation and the second to relate krwith saturation. The van Genuchten model is used here. The subscript F (M) denotes fracture

(matrix) properties. The term SFM describes the flow between fractures and matrix, where A is

6

the fracture/matrix interfacial area, h is a modifying factor [0,1], and kfm is the conductivity fortransfer between matrix and fracture system. In METRA, the relative permeability forfracture-matrix transfer is defined as the upstream value. If flow is from matrix to fracture, thematrix value is used. If flow is in the other direction, the fracture values are used. Kfm is taken asthe harmonic average of the fracture and matrix after appropriately weighting by the twodistances (fracture aperture, and average matrix block size). In practice, this is essentially thesame as using the matrix permeability for Kf, and one-half the matrix block size for d. Thisapproximation is used in constructing the target solution (but not in METRA).

The author is unaware of analytical solutions to Richards equation in dual-permeability mediawith van Genuchten's model for capillary pressure. The target solution was constructednumerically using the Mathematica software system. The numerical approach used a shootingmethod. Specifically, flux and pressure head were specified at the bottom boundary and thein-built solver for initial value ordinary differential equations NDSolve was used to solve forpressure head (and thus saturation) in the one-dimensional column. This NDSolve calculationwas called iteratively within the Mathematica FindRoot function so as to adjust the specified fluxto cause the liquid saturation to agree with the specified value at the upper boundary, thussolving the boundary value problem. The Mathematica script used to construct the targetsolution is in the Mathematica Notebook Test2.nb on the attached disk.

4.2.4 Results

The simulation executed to completion without error. Steady-state saturations are shown inFigure 4. The target solution is plotted as solid curves, and the METRA results are shown asindividual data points. The agreement between the two is very good for both matrix andfracture systems. The maximum error is 0.5 percent for the matrix and 1.4 percent forthe fractures.

4.3 Test 3: Drawdown in an Infinite Confined Aquifer


This simulation is designed to test METRA's representation of saturated flow includingcompressibility effects (major capability 3 in Section 2.0). The geometry is one dimensionalradial with specified withdrawal from the center. The permeability of the aquifer is 10-11 m2

(1.08 1 -10 Wf2), the porosity is 0.2, and the specified withdrawal rate is 1 kg/s (2.20 Ibm/s).Compressibility of the background formation is set to zero, and the only compressibilityconsidered is that of water.

4.3.2 Test Input

The test input file is on the accompanying disk: TestCase3ltheis.dat.

7

1

C:0 O.8

~0.6C,)

0.40 2 4 6 8 10

Depth (meters)

Figure 4: Liquid Saturation Versus Depth (Test 2). The MULTIFLO Results Are Shown asIndividual Data Points and the Target Solution Is Shown as Solid Curves. The Two

Overlay Each Other and Are Indistinguishable on this Scale.[Unit Conversion: Multiply by 3.28 to Convert the x-axis to Feet.]


This configuration has a well-known analytical solution by Theis (1935), which follows directlyfrom an analogy with a classical heat transport problem (e.g., see Domenico and Schwartz,1990). Drawdown s is given by

s2= Q W(u)4;.

where Q is the pumping rate, u = r 2 S/4Tt, T is the transmissivity, S is the storativity, r is

distance from the well, and t is time. The function W(u) is the exponential integral given by

W(u)= f dzU Z

4.3.4 Results

The simulation executed to completion without error. Drawdown curves at 52 minutes and525 minutes are shown in Figure 5. The target solution is plotted as solid curves, and theMETRA results are shown as individual data points. The agreement between the two is verygood. Normalizing by the maximum drawdown, the relative error is about 9 percent near theorigin and decreases with increasing radius. The small difference is most likely due to the factthat the Theis equation requires the compressibility of water to be approximated as a constant,whereas METRA uses the full equation-of-state of water to determine compressibility.

8

(,,14I 12E 10:8o 6 525 minutes} 4 52 minutes

4

0 500 1000 1500 2000Distance from well (meters)

Figure 5: Drawdown Versus Distance from Well at Two Different Times (Test 3).The Multiflo Results Are Shown as Individual Data Points and the Target

Solution Is Shown as Solid Curves.[Unit Conversion: Multiply by 3.28 to Convert the meters to feet.]

4.4 Test 4: Equilibrium Speciation in GEM


This simulation is designed to test GEM's representation of equilibrium speciation for aqueousand gaseous species at 25 0C (77 'F), thus testing major capability 5 in Section 2.0. Thereaction system is written in MULTIFLO format as

0 - h+-+ h2o -oh-

0 • h + hco- -h 2o-co 2(aq)

0 - h+ + hco-3 c3

0 • ca2+ - h+ + hco3 - caco3(aq)

0 h+ + hco- - h2 o -co 2 (9)

where the symbol 0 refers to the null species. In addition, the solution is set to be in equilibriumwith calcite mineral. The geometry is one dimensional with two blocks. Transport is by diffusiononly and the initial and boundary conditions are identical.

9


The test input and output files are on the accompanying disk in directory TestCase4.


Transport is by diffusion only and the initial and boundary conditions are identical. Under theseassumptions, the system is started in steady state and should remain in steady state. Thecalculated activities should be consistent with the mass action equations. The mass actionequation for the r-th reaction is

Keq = fi a Virr i=1

where Keq is the equilibrium constant for the r-th reaction, a, is the activity for the i-th speciesand v denotes the stochiometric matrix.

Activity coefficients in MULTIFLO/GEM are calculated from an extended Debye-Huckel relation

log ri = - Z.Ai +bI1+ai Bali

where A, B and b are parameters, ai represents the hydrated ionic radius of the i-th species, z;is the charge of the i-th species, and I is the ionic strength of the solution.

4.4.4 Results

The simulation ran to completion without error. Calculated concentrations remain identical to theinitial and boundary conditions.

Comparisons between the input value for the equilibrium constants and the equilibrium constantsas calculated from the output activities are shown in Table 3. The values are in agreement.The simulation ran to completion without error.

Activity coefficients as calculated from MULTIFLO/GEM are compared with an extendedDebye-Huckel relation in Table 4.

4.5 Test 5: Solute Transport in Dual Permeability Media


This simulation is designed to test GEM's representation of advective/diffusive transport in dualpermeability media (major capability 4 in Section 2.0). The configuration involves constant flow

10

0

Table 3. Input Values for Equilibrium Constants Compared with Values Calculated fromthe Simulation Output for Test 4

Reaction Input Keq Calculated Keq

oh= - h+ + h2o 14.00 14.00

co2(aq) =h + hco- - h2o -6.345 -6.345

co= - h+ + hco- 10.33 10.33

caco3(aq) ca2+ - h+ + hco- 7.002 7.002

co2(g) = h+ hco - h2 o-7.814 -7.814

Table 4. Activity Coefficients from Test 4 Compared with Hand Calculations

Species Activity Coefficient (target) Activity Coefficient (GEM)

ca2+ 0.7063 0.7063

h+ 0.9227 0.9227

hco3- 0.9131 0.9131

cl- 0.9110 0.9110

in one dimension with flow in both the fractures and matrix. Transport is by advection anddiffusion with first order mass exchange between the fracture and matrix system. At t = 0, theinlet concentration for matrix and fractures is set to 10 times the initial concentration. Parametersfor the flow-through problem are given in Table 5.


The test input file is on the accompanying disk: TestCase51masin1.inp


The author is unaware of analytical solutions to transport in dual permeability media. Asemi-analytical solution was developed, as described in Appendix A. Specifically, a analyticalsolution was obtained in the Laplace domain. Time-domain solutions were then obtained bynumerical inverse Laplace transform. The Mathematica notebook used to obtain the targetsolution is on the accompanying disk (Test5.nb).

11

Table 5. H.rological Parameters for Test 5

Parameter Value

Matrix porosity 0.11

Fracture porosity (internal) 0.11

Fracture volume fraction 0.11

Matrix block size 0.1 m (0.328 feet)

Fracture-to-matrix area reduction factor 1 -6

Fracture saturation 0.5

Matrix saturation 0.5

Darcy velocity in fractures 1 m/year (3.28 ft/year)

Diffusion coefficient 31.5 m2/year (339 ft2/year)

4.5.4 Results

The test ran to completion without error. Results are shown in Figure 6. The target solutions areshown as curves and the test results are shown as individual data points. The test results overlaythe target solution and the two are indistinguishable on this scale. The maximum relative error is4.6 percent for the fractures and 1.2 percent for the matrix.

4.6 Test 6: Three-Dimensional Advective/Dispersive Transportin GEM


The test case tests the transport in GEM in three dimensions (major capability 4 in Section 2.0).The velocity field is uniform and constant with flow directed in the x direction. The initialconcentration is 0.0008 mol/liter (3.94 10-6 mol/in3). At t = 0, the concentration on a small "patch"at the inlet was increased by a factor of ten, and the system is allowed to evolve for 1 year. Aconstant darcy velocity of 1 m/yr (3.28 ft/yr) in the x direction and a diffusion coefficient of3.15 m2/yr (33.9 ft2/yr) is used. The system size is 40 x 11 x 11 cells, with a nonuniform spacingin each direction.


The test input and output files are on the accompanying disk in the directory TestCase6. Theinput file was modified slightly from that specified in the Validation Test Plan to correct an error inthe input file in the specification of the boundary condition.

12

0 0

0.008

°o 0.006

0 0.002U

0 10 20 30 40Distance from inlet (meters)

Figure 6: Concentration in Mol/liter in Fractures and Matrix (Test 4). The MULTIFLOResults Are Shown as Individual Data Points and the Target Solution Is Shown as Solid

Curves. The Two Overlay Each Other and Are Nearly Indistinguishable on this Scale.

[Unit Conversion: Multiply by 0.016 to Convert mol/liter to mol/in 3.]


Analytical solutions for the situation of interest are given by Sagar (1 982) and Wexler (1 991).

For a rectangular patch source centered at the origin extending from (0, Y1, Zd to (0, Y2, Z2), the

analytical solution is 0.002 matrix ~ ~ 2

( sy~zt)= C0 X XP[ t r-3/2 ep-v r _x0 10D 20 3 40

erfc: - erfc; 2 l erfcF --erfc 2 l d-l L2+/5tj L2FDis t f2rm t ( 2m 5ters

Here D is the diffusion coefficient, v is the transport velocity, and Z is a dummy variable.

4.6.4 Results

The simulation ran to completion without error. One-dimensional traces extracted from the

MULTIFLO output are compared with the target solution in Figure 7. When normalized by the

maximum concentration, the maximum error is 5 percent. The error is much smaller for most

locations. The cause of the error is numerical dispersion on the relatively coarse grids of this

simulation.

13

.' 0.006o 0.005 yO z~ oE, 0.004 t y=Oz=0.3

0.003c 0.002

0.001 \ O,z=0.475 2

o 1 2 3 4Distance from inlet, x (meters)

Figure 7: One-Dimensional Traces of Concentration from the Three-DimensionalFlow-Through Test (Test 6). The MULTIFLO Results Are Shown as Individual Data Points

and the Target Solution Is Shown as Solid Curves. The Two Overlay Each Other and AreNearly Indistinguishable on this Scale.

[Unit Conversion: Multiply by 0.016 to Convert mol/liter to mol/in3. Multiply by 3.28 toConvert meters to feet.]

4.7 Test 7: Fully Coupled Flow/Transport with Mineral Dissolutionand Permeability Modification


This simulation tests the coupling between METRA and GEM and kinetically controlled mineral

reactions in GEM (major capability 6 in Section 2.0). The geometry is a one-dimensional "flowthrough" configuration with constant pressure drop across the modeled region. The system

contains only quartz initially in equilibrium with sio2(aq). At t= 0, the concentration at the inlet isdecreased by a factor of 10. The pressure drop across the system is held constant. As themineral dissolves, both the permeability and velocity increase as a result.

Three scenarios are considered. In the first scenario, the simulation ends before the mineral is

dissolved fully at the inlet, transport is by a combination of advection and diffusion, and a

power-law relationship with exponent of 2 is used to relate permeability to porosity, as describedin the MULTIFLO Users Manual. The second scenario is similar to the first except that the

simulation time is longer, thereby allowing full dissolution of the mineral at the inlet, and transport

is by advection only. The third scenario is the same as the second, except that no permeabilitymodification is allowed.

In each scenario, the initial quartz fraction is 50 percent, the porosity is 10 percent, and 40

percent of the volume is assumed to be non-reactive. The initial velocity is 3.1 m/yr (10.2 ft/yr).

14


The test input and output files are on the accompanying disk. For Scenario 1, the METRA andGEM input files are TestCase7lmulti92.dat and TestCase71masin92.inp, respectively. ForScenario 2, the input files are TestCase7kmulti81.dat and TestCase7kmasin81.inp. ForScenario 3, the input files are TestCase 7multi8O.dat and TestCase7lmasin8O.inp.


A new analytical solution to the coupled flow-through problem with dissolution is described inAppendix B and implemented in the Mathematica notebook, Test7.nb, which is on theattached disk.

4.7.4 Results

The tests ran to completion without error. Results are shown in Figure 8a for Scenario 1 and inFigure 8b for Scenarios 2 and 3. The target solution is shown as solid curves and the results of

the MULTIFLO simulations are shown as individual data points. The agreement with the targetsolution is excellent for each scenario. The error relative to the initial mineral abundance is0.8, 1.5, and 1.4 percent for Scenarios 1, 2, and 3, respectively.

4.8 Test 8: Unstructured Grid Capability


The test case tests the unstructured grid capability (major capability 7 in Section 2.0). The test

case is the same as Test Case 3 of Section 5.3, but implemented as an unstructured grid.


The test input and output files are on the accompanying disk in the directory TestCase8.


The target solution is given in Section 5.3.3.

4.8.4 Results

The test ran to completion without error. Results are shown in Figure 9. Agreement with theanalytical solution is very good. Discrepancy between the target solution and simulation result isthe same as in Test Case 3.

15

0

C00coL.

75

'4-sC'

:3a00E

C',

a

0.5

0.4

0.3

0.2

0.1

0

0.5

0.4

0.3

0.2

0.1

0

5 10 15 20 25 30

5 10 15 20 25Distance from inlet (meters)

30

Figure 8: Quartz Volume Fraction Versus Distance from Inlet for the Three Scenarios ofTest 6. The MULTIFLO Results Are Shown as Individual Data Points and the Target

Solution Is Shown as Solid Curves.[Unit Conversion: Multiply by 3.28 to Convert meters to feet]

16

-~14.12

E10c8

0 6 525 minutes4 52 minutes

0 500 1000 1500 2000Distance from well (meters)

Figure 9: Drawdown Versus Distance from Well at Two Different Times (Test 8). TheMULTIFLO Results Are Shown as Individual Data Points and the Target Solution

Is Shown as Solid Curves.[Unit Conversion: Multiply by 3.28 to Convert the meters to feet]

5 KNOWN PROBLEMS

The vapor-pressure lowering variant of Test 1 exhibited a numerical instability at hightemperatures. The temperatures at which the instability appears are outside the range expectedin the repository proposed for Yucca Mountain, Nevada. Consequently, the instability will haveno impact on regulatory activities.

6 CONCLUSIONS

With the minor exception listed in Section 6, results of the validation tests were consistent withthe expected results, thereby providing confidence that the major capabilities probed by thesetests are correctly implemented in MULTIFLO.

The minor problem noted in Section 6 manifest under conditions different from those expected inthe repository proposed for Yucca Mountain, Nevada. Consequently, this problem will have noimpact on regulatory activities.

7 REFERENCES

Bear, J. Dynamics of Fluids in Porous Media. New York City, New York: DoverPublications. 1972.

Domenico, P.A. and F. W. Schwartz. Physical and Chemical Hydrogeology. New York City,New York: John Wiley and Sons. 1990.

17

* S

Doughty, C. and K. Pruess. "A Similarity Solution for Two-Phase Water, Air, and Heat Flow Neara Linear Heat Source in a Porous Medium." Journal of Geophysical Research. Vol. 97, No. B2.pp. 1,821-1,838. 1992.

Lichtner, P.C. "Continuum Formulation of Multicomponent-Multiphase Reactive Transport."Reactive Transport in Porous Media. P.C Lichtner, C.l. Steefel, and E.H. Oelkers, eds.Washington, DC: Mineralogical Society of America. 1996.

Painter, S. "Software Validation Test Plan for MULTIFLO Version 1.5.1." San Antonio, Texas:CNWRA. 2002.

Painter, S., P.C. Lichtner, and M.S. Seth. "MULTIFLO User's Manual: Two-PhaseNonisothermal Coupled Thermal-Hydrological-Chemical Flow Simulator." MULTIFLOVersion 1.5. San Antonio, Texas: CNWRA. 2001.

Sagar, B. "Dispersion in Three Dimension: Approximate Analytical Solutions." AmericanSociety of Civil Engineers, Journal of Hydraulics Division. Vol. 108. 1982.

Theis, C.V. "The Relation Between the Lowering of the Piezometric Surface and Rate andDuration of Discharge of a Well Using Groundwater Storage." Transactions. AmericanGeophysical Union. Vol. 2. pp. 519-524. 1935.

Wexler, E. "Analytical Solutions for 1-, 2-, and 3-Dimensional Solute Transport in Ground-WaterSystems with Uniform Flow." U.S. Geological Survey Report TWRI 3-B7. 1991.

18

0

APPENDIX A

SEMI-ANALYTICAL SOLUTION FOR TEST CASE 5

The configuration involves constant flow in the z direction with flow in both the fractures andmatrix. Transport is by advection and diffusion, with first order mass exchange between thefracture and matrix system. The inlet concentration for matrix and fractures is set to 10 times theinitial concentration at t = 0.

A semi-analytical approach was developed and implemented in the Mathematicae system(Wolfram, 1999). The mass balance equations in one-dimension are

[7SC| = D 2 - V a- a[CC-CF,]

48FVF SFCF ] =DF 2 VFF , +a[C-CF]

where (P is the porosity, S the saturation, C the concentration, D the diffusion coefficient, and vthe velocity. The subscript F denotes the fracture system. The symbol e refers to the fracturevolume fraction. The e multiplying the fracture velocity is a result of the way block areas arecalculated in GEM. The diffusion coefficient for the fracture system is DF = 'PFSF-FDO wherethe tortuosity has been set to 1. The diffusion coefficient for the matrix is the same except that itis missing the efactor.

The diffusional coupling term is a = pSD2A where A is the fracture/matrix interfacial area per unitd

volume, and d is the matrix block size (presumed constant). This expression neglects thefracture aperture relative to the grid block size. For constant properties, this system becomes,

C= Do _2 - d a-[C-CF]cOt gX2 S OX

9fCF t9CF VF £ 9CF~arcdCF= Do g2F + al[C- CF]Ot VF~2SF O9X

2DAa, =-

d

_2DA FSa2 =-d V

d h F SF tF

Taking the Laplace transform of the above, and applying the initial condition C(O)=CF(O)=O.,

A-1

'26 25 .acsC = D - V d' - al[C - CF]

SCF = D d2 -VF- -x+a 2 [C-CF]

with initial conditions C(0) = Co/s and CF(O)= CFO!S and bounded at positive infinity. This

system has the solution,

4(x; s) = c1u 1exp [21x] + c 2u 2exp[22 X]

-i\ C £9C ____"where Ax; s) = (C,-, CF, I , Al and 22 are the negative eigenvalues, and ul and u2o~x £9x J

the corresponding eigenvectors of the matrix

0 1 0 0s+a 1 V -a 1 o

D D Do o 0 1

-a 2 VF S+ a2

D D D

c, and c2 are constants calculated so that the boundary conditions at x = 0 are met. Thecalculation of the eigenvalues and eigenvectors is done using a Mathematica scriptFloThruDCM.nb. Once the solution is constructed this way in the Laplace domain, a numericalinverse Laplace transform is performed to obtain the solution in the time domain.

REFERENCE

Wolfram, S. The Mathematica Book. 4 th Edition. New York City, New York: WolframMedia/Cambridge University Press. 1999.

A-2

APPENDIX B

ANALYTICAL SOLUTION FOR TEST CASE 7

Consider a one-dimensional system with Si0 2(aq) initially in equilibrium with quartz. At t = 0, theconcentration at the inlet is decreased by a factor of 10. The pressure drop across the system isheld constant. As the mineral dissolves, the permeability and velocity increase as a result.Considered two situations where it is possible to get an approximate solution: in Scenario 1,the mineral is not allowed to fully disappear at the inlet, while in Scenario 2, the problem isadvection dominated. In both situations, the quasi-stationary state approximation of Lichtner(1996) was used. Specifically, the characteristic time for mineral dissolution was much largerthan the time required for the aqueous concentration to reach equilibrium. Thus the aqueousconcentration is assumed to be stationary, or more precisely, to be described by a sequence ofquasi-stationary states.

The aqueous concentration C(x,t) is governed by the following equation

£9 X9 e92Cd C dC _ OD d C = _k's(CCeq)H(X ?t))

where q is the porosity, V is the darcy velocity, Ceq is the equilibrium concentration, D is the

diffusion coefficient, s is the specific surface area, and k' = k / Ceq , where k is the reaction

rate. H(.) is the Heaviside function. Quartz is dissolving and will eventually dissolve fully; e(t)is the width of the fully dissolved region.

The mineral volume fraction is given by

605 = V-sk's(C - Ceq ) H (x - t(t))d t

where Vs is the molar volume for the mineral. The initial and boundary conditions are:

C(xt = 0) = Ceq

C(x = Ot)= CO

B-1

0 0

Mineral Not Fully Dissolved at Inlet

If the mineral has not fully dissolved at the inlet, e(t) = 0 , the concentration is stationary, and

we can neglect the time derivative in the above equation for aqueous concentration. The time

required for the mineral to dissolve at the inlet is Ts = S . The equation has solutionk'sACVs

C(X, t) - Ceq = (Co - Ceq)exp x 2- D 1 + ) 1

if advection dominates, this is approximately

C(x, t) - Ceq = (CO - Ceq )exp [ ' x]

k'sThese solutions are found in Bear (1972, p. 631). Note, that Bear's A is-. The mineral

V

volume fraction has solution

Os(x,t) = 0°[1 - exp(- qx) t I rs]

where

v 1 4k s6Dq = D1+ -

If no permeability modification is allowed, the velocity is fixed in the above equation.

If permeability modification is allowed, the velocity will change. The effect of this velocity change

can be accounted for in an approximate way by replacing the velocity V with a time averaged

velocity V, which is calculated as follows. At time t we have from the condition of fixed pressuregradient in one dimension,

V ! 1L ko dxo-V L~o~ k

where the latter term on the left is the ratio of initial permeability ko to effective permeability at

time t. The permeability change is calculated from the porosity change according to a power-law(other relationships are possible but are not considered here):

B-2

---

0*~~~~~~~- L

ko = ( Oo________S° _ m

k [o LR- 0,° - exp(- qx) t /s j

where SR is the reactive volume fraction. The velocity appearing in q here is not v(t) but the

time-averaged velocity. This can be approximated as v = (v0 + v) / 2, which implies

v = 27-v0 .

Substituting v = 2V - v0 and for ° in the integrand, and then calculating the integral

explicitly yields the following equation:

V0 + b +(b+a exp(Lq))Iog(b+a exp(Lq)) b+(b+a)log(b+a)_O

2V--vo (b+a exp(Lq))q (b+a)q

Here, the effective (time averaged ) velocity is to be used in the expression for q, not v(t). Thisequation is then to be solve for V . This result is specific to the situation m = 2. Note

a =R- 0S and b = tVsk'sAC.

Once the time-averaged velocity is obtained, it is used in place of V in the expression for themineral volume fraction.

Advection Dominated Case

The preceding analysis applies when the mineral has not completely disappeared at the inlet.This analysis is difficult to extend to the more general situation of a moving boundary in thegeneral case, but can be extended if we restrict our consideration to the advection dominatedcase. The solution in this situation is given, for example, in Lichtner (1996, p. 51)

C(xt) - Ceq = (C0 - Ceq) ex[ -kL's(X -( (t)1

where

q(t) = 9°_ (t__s)

Similarly, the mineral volume fraction is given by:

(x, t) = 0 (1 - exp k[- v(x - IN)

B-3

0 0

Continuing as before, the following equation is obtained;

vo b+(b+aexp(L'q))log(b+aexp(L'q)) b+(b+a)lo°(b+a) (#Ofm e(t) o

2V -vo (b+a exp(L q))q (b+a)q iR

where q(v) = - b = Vsk'sAC , L' = L - 4(t), and the time average velocity is to be used

in place of v in t(O . This equation is to be solved for the time averaged velocity, which

replaces the velocity in the equation for the mineral volume fraction.

REFERENCES

Bear, J. Dynamics of Fluids in Porous Media. New York City, New York: DoverPublications. 1972.

Lichtner, P.C. "Continuum Formulation of Multicomponent-Multiphase Reactive Transport."Reactive Transport in Porous Media. P.C. Lichtner, C.L. Steefel, and E.H. Oelkers, eds.Washington, DC: Mineralogical Society of America. 1996.

B-4

07. element managerapprval: - c date iti

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